The [tex]\boxed{\Delta {\text{VTU and }}\Delta {\text{CAB}}}[/tex] are congruent by AAS congruency criterion. Option (a) is correct.
Further Explanation:
The congruent triangles are those in which all the corresponding angles and the sides are equal.
There are many congruency rules and are as follows.
1. Angle Angle Side (AAS)
2. Angle Side Angle (ASA)
3. Side SideSide (SSS)
4. Side Angle Side (SAS)
Given:
The options are as follows,
(a). [tex]\Delta {\text{VTU and }}\Delta {\text{CAB}}[/tex]
(b). [tex]\Delta {\text{VTU and }}\Delta {\text{HFG}}[/tex]
(c). [tex]\Delta{\text{ HFG and }}\Delta {\text{CAB}}[/tex]
(d). None of the above.
Explanation:
In [tex]\Delta {\text{VTU and }}\Delta {\text{CAB}},[/tex]
[tex]\begin{aligned}\angle {\text{UVT}}&= \angle {\text{BCA}}\\\angle {\text{VTU}}&= \angle {\text{CAB}}\\{\text{AB}}&= {\text{TU}}\\\Delta {\text{VTU}} \cong \Delta {\text{CAB}}\left( {{\text{AAS congruency}}} \right)\\\end{aligned}[/tex]
The [tex]\boxed{\Delta {\text{VTU and }}\Delta {\text{CAB}}}[/tex] are congruent by AAS congruency criterion. Option (a) is correct.
Option (b) is not correct.
Option (c) is not correct.
Option (d) is not correct.
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Triangle
Keywords: congruent, angles, triangle, ASA, angle side angle, congruent sides, acute angle, side, corresponding angles, congruent triangle.
